Capturing steep transitions in high-Reynolds fluid flows and rogue wave systems via a dual-channel wavelet neural operator

Purpose This study aims to propose a novel deep operator learning framework, the dual-channel Multi-Scale Attention Wavelet Neural Operator (dcMAWNO), specifically designed for high-fidelity modeling of steep transitions in nonlinear fluid flows, such as shock waves in the high-Reynolds-number viscous flows as well as solitons, rogue waves and turbulent structures that are the phenomena in the compressible, dispersive and chaotic hydrodynamic systems. Design/methodology/approach dcMAWNO integrates multi-scale wavelet decomposition with channel-wise attention mechanisms to decouple smooth background fields from localized high-gradient regions. It applies adaptive refinement exclusively to transitional zones while preserving the accuracy in quiescent areas. The model is trained and validated on three canonical systems: the viscous Burgers’ equation, the Korteweg–de Vries (KdV) equation, and the two-dimensional incompressible Navier–Stokes equations at the viscosity ν < 10-4, whereby long-term prediction is enabled from t ∈ [0,10] to [20,30]. Comprehensive comparisons on benchmarks against Fourier Neural Operators (FNO) and Deep Operator Networks as baselinve are included. Findings Numerical experiments demonstrate that dcMAWNO resolves shock fronts with minimal numerical diffusion and accurately tracks their propagation speed and position. In KdV systems, it captures both multi-soliton interactions and the spontaneous formation of rogue waves from stochastic initial conditions. For the high-Reynolds turbulence, dcMAWNO exhibits significantly slower error growth over long-time prediction horizons compared to FNO, while maintaining energy spectrum fidelity and reducing spurious oscillations. Originality/value dcMAWNO is a dual-channel neural operator that explicitly separates high- and low-frequency components via wavelet transforms to model smooth backgrounds and steep structures, such as shocks, rogue waves and turbulent eddies, enabling accurate, stable and efficient long-time prediction. It holds promise for climate modeling, ocean engineering and resilient infrastructure, aligning with the United Nations Sustainable Development Goals.